This paper investigates the problem of efficient constrained global optimization of hybrid models that are a composition of a known white-box function and an expensive multi-output black-box function subject to noisy observations, which often arises in real-world science and engineering applications. We propose a novel method, Constrained Upper Quantile Bound (CUQB), to solve such problems that directly exploits the composite structure of the objective and constraint functions that we show leads substantially improved sampling efficiency. CUQB is a conceptually simple, deterministic approach that avoid constraint approximations used by previous methods. Although the CUQB acquisition function is not available in closed form, we propose a novel differentiable sample average approximation that enables it to be efficiently maximized. We further derive bounds on the cumulative regret and constraint violation under a non-parametric Bayesian representation of the black-box function. Since these bounds depend sublinearly on the number of iterations under some regularity assumptions, we establis bounds on the convergence rate to the optimal solution of the original constrained problem. In contrast to most existing methods, CUQB further incorporates a simple infeasibility detection scheme, which we prove triggers in a finite number of iterations when the original problem is infeasible (with high probability given the Bayesian model). Numerical experiments on several test problems, including environmental model calibration and real-time optimization of a reactor system, show that CUQB significantly outperforms traditional Bayesian optimization in both constrained and unconstrained cases. Furthermore, compared to other state-of-the-art methods that exploit composite structure, CUQB achieves competitive empirical performance while also providing substantially improved theoretical guarantees.

翻译：本文研究了在噪声观测条件下，对由已知白箱函数与昂贵多输出黑箱函数组成的混合模型进行高效约束全局优化的问题，这在现实科学与工程应用中频繁出现。我们提出了一种新颖方法——约束上分位数界（CUQB）以解决此类问题，该方法直接利用目标函数与约束函数的复合结构，我们证明了这能显著提升采样效率。CUQB是一种概念简洁的确定性方法，避免了先前方法所使用的约束近似。尽管CUQB采集函数无闭式解，我们提出了一种新颖的可微样本均值近似方法，使其能够被高效最大化。进一步地，我们在黑箱函数的非参数贝叶斯表示下推导了累积遗憾与约束违背的界。由于这些界在一些正则性假设下随迭代次数呈次线性增长，我们建立了原始约束问题最优解收敛速率的界。与多数现有方法不同，CUQB进一步集成了简单的不可行性检测机制，我们证明当原始问题不可行时，该机制能在有限迭代次数内（在贝叶斯模型下以高概率）被触发。在包括环境模型校准与反应器系统实时优化在内的多个测试问题上的数值实验表明，CUQB在约束与无约束情形下均显著优于传统贝叶斯优化。此外，相较于其他利用复合结构的先进方法，CUQB在实现具有竞争力的实证性能的同时，还提供了大幅度改进的理论保证。